1. **Stating the problem:** Given the data set: 8, 6, 5, 9, 7, 6, 4, 5, 3, find the interquartile range (IQR). 2. **Formula and explanation:** The interquartile range is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$): $$\text{IQR} = Q_3 - Q_1$$ Quartiles divide the data into four equal parts after sorting. 3. **Sort the data:** Sorted data: 3, 4, 5, 5, 6, 6, 7, 8, 9 4. **Find the median (second quartile, $Q_2$):** Number of data points $n=9$ (odd), median is the middle value: $$Q_2 = \text{5th value} = 6$$ 5. **Find $Q_1$ (median of lower half):** Lower half (below median): 3, 4, 5, 5 Median of these 4 values: $$Q_1 = \frac{4^{th} + 2^{nd}}{2} = \frac{4 + 5}{2} = 4.5$$ 6. **Find $Q_3$ (median of upper half):** Upper half (above median): 6, 7, 8, 9 Median of these 4 values: $$Q_3 = \frac{6^{th} + 8^{th}}{2} = \frac{7 + 8}{2} = 7.5$$ 7. **Calculate IQR:** $$\text{IQR} = Q_3 - Q_1 = 7.5 - 4.5 = 3$$ **Final answer:** The interquartile range of the data is **3**.